Question

(x+2)/(1-2x)=2x Help

Answer 1

ОДЗ: x≠0,5

(x+2)/(1-2x) -2x=0

x+2-2x(1-2x)=0

x+2-2x+4x²=0

4x²-x+2=0

D= 1-32= -31

D<0 - действительных корней нет

Answer 2

х≠1/2, тогда знаменатель обращается в нуль. Приведем к общему знаменателю обе части уравнения.

х+2=2х*(1-2х); х+2=2х-4х²; 4х²- 2х=-2-х; 4х²-х+2=0; Дискриминант равен

1-32=-31, действительных корней нет.

Answer 3

To solve the equation:

(x + 2)/(1 - 2x) = 2x

Let's begin by simplifying the expression:

Multiply both sides of the equation by (1 - 2x) to eliminate the fraction:

(x + 2) = 2x(1 - 2x)

Expand the right side:

x + 2 = 2x - 4x^2

Rearrange the terms:

0 = -4x^2 + x + 2

Now, we have a quadratic equation in standard form. To solve for x, we can use factoring, completing the square, or the quadratic formula.

In this case, let's solve it using the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac))/(2a)

For our equation 0 = -4x^2 + x + 2, a = -4, b = 1, and c = 2. Plugging these values into the quadratic formula, we get:

x = (-(1) ± √((1)^2 - 4(-4)(2)))/(2(-4))

Simplifying further:

x = (-1 ± √(1 + 32))/(-8)

x = (-1 ± √33)/(-8)

Hence, the solutions for the equation (x + 2)/(1 - 2x) = 2x are:

x = (-1 + √33)/(-8) x = (-1 - √33)/(-8)

Please note that these solutions might be approximate values depending on the exact values of √33.